AN IMPROVED PEDAGOGICAL APPROACH TO TEACHING THE THEORY OF ELEMENTARY FUNCTIONS

Abstract

This article recommends teaching the elements of mathematical analysis in schools as the theory of elementary functions. It proposes changing the traditional sequence of topics — “Limit of a sequence, limit of a function, derivative, and integral” — to the following order based on the properties of elementary functions: “Limit of a sequence, limit, derivative, and integral of a continuous function.” The simplification of the traditional approach was achieved by modifying the didactic axiom confirming the continuity of elementary functions and, consequently, adapting the conditions in Heine’s definition of function continuity. In our opinion, this pedagogical approach helps to reduce theoretical gaps and eliminate the difficulties inherent in traditional teaching methods. This work can be considered a simplified interpretation of Academician A.N. Kolmogorov’s idea that the theory of continuous functions should be taught at school, while the theory of general functions should be studied in higher education. We believe that the proposed project can be effectively applied in developing curricula for both general and specialized schools.